Here is the full list of all 74 Crash Bandicoot N. Sane Trilogy achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Avoid whatever he's flinging at you.
Die.
Shoot 5 of them in a single level.
Have your bazooka ready.
Shoot the Imposter
Just "forget" it. Repeatedly.
Die as Crash.
Don't feel guilty about jumping on him.
Miss a lot of boxes.
Shoot a background UFO in Future Tense.
Defeat 5 enemies with Coco's Savage Hurricane Spin
Defeat 5 enemies with Coco's Double Leg Drop
Defeat 5 enemies with Coco's Spin
Earn the Gems in the bonus levels
Discovered the Secret Exit in Dino Might!
Earn 30 Relics (gold or better)
Discovered the Secret Exit in Road Crash
Earn 42 Gems
Seek and destroy. Again.
Defeat N. Cortex
Defeat N. Gin
Earn 21 Gems
Defeat N. Tropy
Discover a Death Route
Discover a Gem Path after earning a Color Gem
Earn 10 Relics (gold or better)
Defeat Dingodile
Earn 99 Lives
Earn 5 Relics
Defeat Tiny Tiger
Discover a "?" Bonus Path
Discover the Secret Exit in Diggin' It
Discover the Secret Exit in Air Crash
Discover the Secret Exit in Bear Down
Earn 27 Relics (gold or better)
Unlocked the Secret Exit in Unbearable
Unlocked the Secret Exit in Hangin' Out
Defeat the Komodo Brothers
Fly, then die.
Defeat Ripper Roo
Earn 26 Relics (gold or better)
Do hard time
Seek and destroy
Earn 26 Gems
Defeat N. Brio
Earn the Key in Jaws of Darkness
Defeat Pinstripe Potoroo
Defeat Koala Kong
Earn the Key in Sunset Vista
Earn 13 Gems
Defeat Papu-Papu
Spin away an Extra Life
Enter a Bonus Round after collecting 3 Character Tokens
In a single level, spin an enemy into another enemy twice